TRENTON, N.J. (AP) -- They've bickered over whether she knew he was gay, whose tell-all book would sell better, whether a poster of a nude man hanging over his new lover's bed had to come down before she'd allow their 6-year-old to visit.

When Jim and Dina Matos McGreevey head back to court Friday for the umpteenth round in their drawn-out divorce proceeding, they'll argue over whether she has to cooperate with the experts he hired to bolster his claim for shared custody.

New Jersey's estranged former first couple is headed for a May trial unless they resolve the custody and money issues that have arisen since their acrimonious parting. They split three months after he came out on live television, acknowledging a gay affair with an ex-staffer and saying he would resign as governor.

"She is a betrayed spouse, but worse," said Raoul Felder, a celebrity divorce lawyer who is not involved in the McGreevey case. "He turned away from her for a member of his own sex; it was even more insulting because she was made a public fool. She feels as if she was used and this is payback time."

Felder, whose list of clients includes exes of Mike Tyson and Liz Taylor, doubts that the former governor and his wife will follow the script of the 95 percent of divorcing spouses who settle their cases before trial.

"There seems to be a large dose of people not acting particularly reasonably and responsibly," said Mark H. Sobel, an experienced Woodbridge divorce lawyer who is familiar with this case though not handling it. "It doesn't seem likely that reasonable people could not work out the logistics of a birthday party."

The latter refers to daughter Jacqueline McGreevey's 6th birthday bash in December. Her parents rushed in to court two days before the party after a squabble over whether the party could go on at Jim McGreevey's house since it wasn't his weekend for visitation.

McGreevey said his legal expenses have topped $400,000 so far and that they easily could double before the divorce is final. Matos McGreevey and her lawyer, John Post, did not return messages seeking comment.

The McGreeveys were married in October 2000 and split in November 2004, when they left the governor's mansion in Princeton and began living apart. As of February, they've been separated with the intention of divorcing for three years and three months -- nearly as long as the marriage.

After the breakup, he wrote a tell-all book, then went on "The Oprah Winfrey Show" and acknowledged having a gay tryst while his wife was in the hospital giving birth to their daughter.

She followed with a tell-all book of her own, and they argued over whose would sell more copies.

Through their lawyers -- he's on his third, she's kept the same one throughout -- they've squabbled over all manner of other issues in court papers:

-- Jacqueline should not be allowed to sleep in her father's bed, Matos McGreevey said.

-- The child should be able to participate in Episcopal services when she's with him, he said.

-- He should get the child for overnight visits on a school night, he said.

-- McGreevey, a licensed attorney, is not living up to his earning potential, she claimed.

-- His boyfriend, Mark O'Donnell, should have to disclose his finances and business dealings, she insisted.

McGreevey was a rising star in New Jersey Democratic politics until the gay sex scandal toppled him swiftly and unexpectedly. Today, he lives with his money-manager partner in Plainfield and is studying for the Episcopal priesthood.

Matos McGreevey lives in a modest home in Springfield. She is an executive with Columbus Hospital, but likely will lose her job in the spring when the hospital is slated to close.